Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

How to compute the Wedderburn decomposition of a finite-dimensional associative algebra

How to compute the Wedderburn decomposition of a finite-dimensional associative algebra This is a survey paper on algorithms that have been developed during the last 25 years for the explicit computation of the structure of an associative algebra of finite dimension over either a finite field or an algebraic number field. This constructive approach was initiated in 1985 by Friedl and Róónyai and has since been developed by Cohen, de Graaf, Eberly, Giesbrecht, Ivanyos, Küüronya and Wales. I illustrate these algorithms with the case n == 2 of the rational semigroup algebra of the partial transformation semigroup PT n on n elements; this generalizes the full transformation semigroup and the symmetric inverse semigroup, and these generalize the symmetric group S n . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Groups - Complexity - Cryptology de Gruyter

How to compute the Wedderburn decomposition of a finite-dimensional associative algebra

Groups - Complexity - Cryptology , Volume 3 (1) – May 1, 2011

Loading next page...
 
/lp/de-gruyter/how-to-compute-the-wedderburn-decomposition-of-a-finite-dimensional-0iI8xuP0NO
Publisher
de Gruyter
Copyright
©© de Gruyter 2011
ISSN
1867-1144
eISSN
1869-6104
DOI
10.1515/GCC.2011.003
Publisher site
See Article on Publisher Site

Abstract

This is a survey paper on algorithms that have been developed during the last 25 years for the explicit computation of the structure of an associative algebra of finite dimension over either a finite field or an algebraic number field. This constructive approach was initiated in 1985 by Friedl and Róónyai and has since been developed by Cohen, de Graaf, Eberly, Giesbrecht, Ivanyos, Küüronya and Wales. I illustrate these algorithms with the case n == 2 of the rational semigroup algebra of the partial transformation semigroup PT n on n elements; this generalizes the full transformation semigroup and the symmetric inverse semigroup, and these generalize the symmetric group S n .

Journal

Groups - Complexity - Cryptologyde Gruyter

Published: May 1, 2011

Keywords: Structure theory of associative algebras; Dickson's Theorem on the radical; Wedderburn––Artin Theorem; Wedderburn––Malcev Theorem; computational algebra; finite transformation semigroups; representation theory of finite semigroups

There are no references for this article.